Do procedural textures save render time and memory?
this is a great question! 

Procedural textures made in Blender do take quite a hit on a render's speed, as well as the memory that is used. This obviously scales with how complex the texture is, so it's difficult to predict exactly how much the texture will slow it down. 

Unfortunately, I don't know the technical details of how procedural textures are computed during a render, so I can't help with that. Maybe someone with more technical experience knows the answer :^)

In general, here are my experiences on the matter. It's normally efficient enough that for general usage you can go ahead and mix noise to your heart's content. If you have very large procedural textures, (let's just go with >100 nodes) it might be worthwhile to 
use Blender's baking functionality to bake them to images. This would be much more important if you plan on doing animations, because the extra time on a single frame get compounded with every other frame that the animation uses.

So ya, I'd say it's generally good! Just know that you can bake them down to images if you plan on doing an animation or something.

I hope this helps, and good luck!